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<a href="_negative_a_u_c_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">//===========================================================================</span><span class="comment"></span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> * </span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> *</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> * \brief       Functions for measuring the area under the (ROC) curve</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> * </span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * </span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> *</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> * \author      Christian Igel</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> * \date        2011</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> *</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> *</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * </span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * </span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * </span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * </span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="comment"> *</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="comment"> */</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#ifndef SHARK_OBJECTIVEFUNCTIONS_NEGATIVE_AUC_H</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#define SHARK_OBJECTIVEFUNCTIONS_NEGATIVE_AUC_H</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &lt;<a class="code" href="_abstract_cost_8h.html" title="cost function for quantitative judgement of deviations of predictions from target values">shark/ObjectiveFunctions/AbstractCost.h</a>&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &lt;<a class="code" href="_key_value_pair_8h.html">shark/Core/utility/KeyValuePair.h</a>&gt;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {<span class="comment"></span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="comment">///</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="comment">/// \brief Negative area under the curve</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="comment">/// </span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">/// This class computes the area under the ROC (receiver operating characteristic) curve.</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/// It implements the algorithm described in:</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno">   47</span><span class="comment">/// Tom Fawcett. ROC Graphs: Notes and Practical Considerations for Researchers. 2004</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">///</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">/// The area is negated so that optimizing the AUC corresponds to a minimization task. </span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">/// \ingroup costfunctions</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment"></span><span class="keyword">template</span>&lt;<span class="keyword">class</span> LabelType = <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>, <span class="keyword">class</span> OutputType = RealVector&gt;</div>
<div class="foldopen" id="foldopen00052" data-start="{" data-end="};">
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html">   52</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_negative_a_u_c.html" title="Negative area under the curve.">NegativeAUC</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_abstract_cost.html" title="Cost function interface.">AbstractCost</a>&lt;LabelType, OutputType&gt;</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>{</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span><span class="keyword">public</span>:</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html#aaaca27d1a2b3d4d5350aa3689ba3b869">   55</a></span>    <span class="keyword">typedef</span> <a class="code hl_struct" href="structshark_1_1_key_value_pair.html" title="Represents a Key-Value-Pair similar std::pair which is strictly ordered by it&#39;s key.">KeyValuePair&lt; double, LabelType &gt;</a> <a class="code hl_typedef" href="classshark_1_1_negative_a_u_c.html#aaaca27d1a2b3d4d5350aa3689ba3b869">AUCPair</a>;</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span><span class="comment"></span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span><span class="comment">    /// Constructor.</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span><span class="comment">    /// \param invert: if set to true, the role of positive and negative class are switched</span></div>
<div class="foldopen" id="foldopen00059" data-start="{" data-end="}">
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html#a8589cb24e741e1934af4a704ec3dd7dc">   59</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a8589cb24e741e1934af4a704ec3dd7dc">NegativeAUC</a>(<span class="keywordtype">bool</span> invert = <span class="keyword">false</span>) {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>        <a class="code hl_variable" href="classshark_1_1_negative_a_u_c.html#ac8ee356a559d98706eeaf115a6affe6d">m_invert</a> = invert;</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>    }</div>
</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span><span class="comment"></span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span><span class="comment">    /// \brief From INameable: return the class name.</span></div>
<div class="foldopen" id="foldopen00064" data-start="{" data-end="}">
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html#a9f47bfe33018e018d4b82dbe03caa3c2">   64</a></span><span class="comment"></span>    std::string <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a9f47bfe33018e018d4b82dbe03caa3c2" title="From INameable: return the class name.">name</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> <span class="stringliteral">&quot;NegativeAUC&quot;</span>; }</div>
</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span><span class="comment"></span> </div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span><span class="comment">    /// \brief Computes area under the curve.</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span><span class="comment">    /// \param target: class label, 0 or 1</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span><span class="comment">    /// \param prediction: prediction by classifier, OutputType-valued vector</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span><span class="comment">    /// \param column: indicates the column of the prediction vector interpreted as probability of positive class</span></div>
<div class="foldopen" id="foldopen00071" data-start="{" data-end="}">
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html#a5265a1b04657e60004f9a681027cfea4">   71</a></span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a5265a1b04657e60004f9a681027cfea4" title="Computes area under the curve.">eval</a>(<a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;LabelType&gt;</a> <span class="keyword">const</span>&amp; target, <a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;OutputType&gt;</a> <span class="keyword">const</span>&amp; prediction, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> column)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(<a class="code hl_function" href="group__shark__globals.html#ga6231b46b09731352a3cac40709a9625f" title="Return the dimensionality of a dataset.">dataDimension</a>(prediction) &gt; column,<span class="stringliteral">&quot;Column number too large&quot;</span>);</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span> </div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        std::size_t elements = target.<a class="code hl_function" href="group__shark__globals.html#ga814e8b0028cc90dd2af69805e8f8a04d" title="Returns the total number of elements.">numberOfElements</a>();</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>        <span class="keywordtype">unsigned</span> P = 0; <span class="comment">// positive examples</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        <span class="keywordtype">unsigned</span> N = 0; <span class="comment">// negative examples</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        std::vector&lt;AUCPair&gt; L(elements); <span class="comment">// list of predictions and labels</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span> </div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>        <span class="keywordflow">for</span>(std::size_t i=0; i!= elements; i++) { <span class="comment">// build list</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            <a class="code hl_typedef" href="classshark_1_1_abstract_cost.html#aa0d1c0437931e46d5b6192b214bc6f59">LabelType</a> t = target.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(i);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>            <span class="comment">// negate predictions if m_invert is set</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            <span class="keywordflow">if</span>(!<a class="code hl_variable" href="classshark_1_1_negative_a_u_c.html#ac8ee356a559d98706eeaf115a6affe6d">m_invert</a>)</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span>                L[i] = <a class="code hl_typedef" href="classshark_1_1_negative_a_u_c.html#aaaca27d1a2b3d4d5350aa3689ba3b869">AUCPair</a>(prediction.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(i)(column), t);</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>                L[i] = <a class="code hl_typedef" href="classshark_1_1_negative_a_u_c.html#aaaca27d1a2b3d4d5350aa3689ba3b869">AUCPair</a>(-prediction.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(i)(column), t);</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            <span class="comment">// count positive and negative examples</span></div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            <span class="keywordflow">if</span>(t &gt; 0) </div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>                P++;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            <span class="keywordflow">else</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                N++;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        }    </div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>        std::sort (L.begin(), L.end(),std::greater&lt;AUCPair&gt;() ); <span class="comment">// sort in decreasing order</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>        <span class="keywordtype">double</span>   A = 0; <span class="comment">// area</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>        <span class="keywordtype">unsigned</span> TP = 0; <span class="comment">// true positives</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>        <span class="keywordtype">unsigned</span> FP = 0; <span class="comment">// false positives</span></div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        <span class="keywordtype">unsigned</span> TPPrev = 0; <span class="comment">// previous true positives</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>        <span class="keywordtype">unsigned</span> FPPrev = 0; <span class="comment">// previous false positives</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>        <span class="keywordtype">double</span>   predictionPrev = -std::numeric_limits&lt;double&gt;::max(); <span class="comment">// previous prediction</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>        <span class="keywordflow">for</span>(std::size_t i=0; i != elements; i++)  {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <span class="keywordflow">if</span>(L[i].key != predictionPrev){</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                A += <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a336caed340dd3d3c82e7149091ce0977">trapArea</a>(FP/<span class="keywordtype">double</span>(N),FPPrev/<span class="keywordtype">double</span>(N),TP/<span class="keywordtype">double</span>(P),TPPrev/<span class="keywordtype">double</span>(P));</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>                predictionPrev = L[i].key;</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>                FPPrev = FP;</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                TPPrev = TP;</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>            }</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            <span class="keywordflow">if</span>(L[i].value &gt; 0) </div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>                TP++; <span class="comment">// positive example</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            <span class="keywordflow">else</span> </div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                FP++; <span class="comment">// negative example</span></div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>        }</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>        <span class="comment">// deviation from the original algorithm description: A += trapArea(1, FPPrev, 1, TPPrev);</span></div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>        A += <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a336caed340dd3d3c82e7149091ce0977">trapArea</a>(FP/<span class="keywordtype">double</span>(N), FPPrev/<span class="keywordtype">double</span>(N), TP/<span class="keywordtype">double</span>(P), TPPrev/<span class="keywordtype">double</span>(P));</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>        <span class="comment">//~ A /= double(N*P);</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>        <span class="keywordflow">return</span> -A;</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>    }</div>
</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span><span class="comment"></span> </div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span><span class="comment">    /// \brief Computes area under the curve. If the prediction vector is</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span><span class="comment">    /// 1-dimensional, the &quot;positive&quot; class is mapped to larger values. If</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span><span class="comment">    /// the prediction vector is 2-dimensional, the second dimension is</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span><span class="comment">    /// viewed as the &quot;positive&quot; class. For higher dimensional vectors, an</span></div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span><span class="comment">    /// exception is thrown. In such a case, the column has to be</span></div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span><span class="comment">    /// explicitly specified as an additional parameter.</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span><span class="comment">    ///</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span><span class="comment">    /// \param target: class label, 0 or 1</span></div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span><span class="comment">    /// \param prediction: prediction by classifier, OutputType-valued vector</span></div>
<div class="foldopen" id="foldopen00130" data-start="{" data-end="}">
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html#a969990014ff8964d6e67fcf72318b02b">  130</a></span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a969990014ff8964d6e67fcf72318b02b" title="Computes area under the curve. If the prediction vector is 1-dimensional, the &quot;positive&quot; class is map...">eval</a>(<a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;LabelType&gt;</a> <span class="keyword">const</span>&amp; target, <a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;OutputType&gt;</a>  <span class="keyword">const</span>&amp; prediction)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(prediction.<a class="code hl_function" href="group__shark__globals.html#ga814e8b0028cc90dd2af69805e8f8a04d" title="Returns the total number of elements.">numberOfElements</a>() &gt;= 1,<span class="stringliteral">&quot;Empty prediction set&quot;</span>);</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(<a class="code hl_function" href="group__shark__globals.html#ga6231b46b09731352a3cac40709a9625f" title="Return the dimensionality of a dataset.">dataDimension</a>(prediction) &lt; 3, <span class="stringliteral">&quot;Can not compute with more than two columns&quot;</span>);</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        std::size_t dim = <a class="code hl_function" href="group__shark__globals.html#ga6231b46b09731352a3cac40709a9625f" title="Return the dimensionality of a dataset.">dataDimension</a>(prediction);</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <span class="keywordflow">if</span>(dim == 1) </div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a5265a1b04657e60004f9a681027cfea4" title="Computes area under the curve.">eval</a>(target, prediction, 0);</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span>(dim == 2) </div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a5265a1b04657e60004f9a681027cfea4" title="Computes area under the curve.">eval</a>(target, prediction, 1);</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>        <span class="keywordflow">return</span> 0.;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span>    }</div>
</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno">  140</span> </div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno">  141</span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno">  142</span><span class="keyword">protected</span>:</div>
<div class="foldopen" id="foldopen00143" data-start="{" data-end="}">
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html#a336caed340dd3d3c82e7149091ce0977">  143</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_negative_a_u_c.html#a336caed340dd3d3c82e7149091ce0977">trapArea</a>(<span class="keywordtype">double</span> x1, <span class="keywordtype">double</span> x2, <span class="keywordtype">double</span> y1, <span class="keywordtype">double</span> y2)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno">  144</span>        <span class="keywordtype">double</span> base = std::abs(x1-x2);</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno">  145</span>        <span class="keywordtype">double</span> heightAvg = (y1+y2)/2;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno">  146</span>        <span class="keywordflow">return</span> base * heightAvg;</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno">  147</span>    }</div>
</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno">  148</span> </div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_a_u_c.html#ac8ee356a559d98706eeaf115a6affe6d">  149</a></span>    <span class="keywordtype">bool</span> <a class="code hl_variable" href="classshark_1_1_negative_a_u_c.html#ac8ee356a559d98706eeaf115a6affe6d">m_invert</a>;</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno">  150</span>};</div>
</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno">  151</span><span class="comment"></span> </div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno">  152</span><span class="comment">///</span></div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno">  153</span><span class="comment">/// \brief Negative Wilcoxon-Mann-Whitney statistic </span></div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno">  154</span><span class="comment">/// </span></div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno">  155</span><span class="comment">/// This class computes the Wilcoxon-Mann-Whitney statistic, which is</span></div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno">  156</span><span class="comment">/// an unbiased estimate of the area under the ROC curve.</span></div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno">  157</span><span class="comment">///</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno">  158</span><span class="comment">/// See, for example:</span></div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno">  159</span><span class="comment">/// Corinna Cortes, Mehryar Mohri. Confidence Intervals for the Area under the ROC Curve. NIPS, 2004</span></div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno">  160</span><span class="comment">///</span></div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno">  161</span><span class="comment">/// The area is negated so that optimizing the AUC corresponds to a minimization task. </span></div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno">  162</span><span class="comment">/// \ingroup costfunctions</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno">  163</span><span class="comment"></span><span class="keyword">template</span>&lt;<span class="keyword">class</span> LabelType = <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span>, <span class="keyword">class</span> OutputType = LabelType&gt;</div>
<div class="foldopen" id="foldopen00164" data-start="{" data-end="};">
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html">  164</a></span><span class="keyword">class </span><a class="code hl_class" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html" title="Negative Wilcoxon-Mann-Whitney statistic.">NegativeWilcoxonMannWhitneyStatistic</a> : <span class="keyword">public</span> <a class="code hl_class" href="classshark_1_1_abstract_cost.html" title="Cost function interface.">AbstractCost</a>&lt;LabelType, OutputType&gt;</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno">  165</span>{</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno">  166</span><span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno">  167</span><span class="comment">    /// Constructor.</span></div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno">  168</span><span class="comment">    /// \param invert: if set to true, the role of positive and negative class are switched</span></div>
<div class="foldopen" id="foldopen00169" data-start="{" data-end="}">
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#a762a1be770ac41de5e0a83d08bc7bc2f">  169</a></span><span class="comment"></span>    <a class="code hl_function" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#a762a1be770ac41de5e0a83d08bc7bc2f">NegativeWilcoxonMannWhitneyStatistic</a>(<span class="keywordtype">bool</span> invert = <span class="keyword">false</span>) {</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno">  170</span>        m_invert = invert;</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno">  171</span>    }</div>
</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno">  172</span><span class="comment"></span> </div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno">  173</span><span class="comment">    /// \brief From INameable: return the class name.</span></div>
<div class="foldopen" id="foldopen00174" data-start="{" data-end="}">
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#a7e5edb29b2a6ac5030b9c71573809971">  174</a></span><span class="comment"></span>    std::string <a class="code hl_function" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#a7e5edb29b2a6ac5030b9c71573809971" title="From INameable: return the class name.">name</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno">  175</span><span class="keyword">    </span>{ <span class="keywordflow">return</span> <span class="stringliteral">&quot;NegativeWilcoxonMannWhitneyStatistic&quot;</span>; }</div>
</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno">  176</span><span class="comment"></span> </div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno">  177</span><span class="comment">    /// \brief Computes Wilcoxon-Mann-Whitney statistic.</span></div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno">  178</span><span class="comment">    /// \param target: interpreted as binary class label</span></div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno">  179</span><span class="comment">    /// \param prediction: interpreted as binary class label</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno">  180</span><span class="comment">    /// \param column: indicates the column of the prediction vector interpreted as probability of positive class</span></div>
<div class="foldopen" id="foldopen00181" data-start="{" data-end="}">
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#aa2f5af11ed9351eb339943a4a0ef2e38">  181</a></span><span class="comment"></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#aa2f5af11ed9351eb339943a4a0ef2e38" title="Computes Wilcoxon-Mann-Whitney statistic.">eval</a>(<a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;LabelType&gt;</a> <span class="keyword">const</span>&amp; target, <a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;OutputType&gt;</a> <span class="keyword">const</span>&amp; prediction, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> column)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno">  182</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(prediction(0).size() &gt; column,<span class="stringliteral">&quot;column number too large&quot;</span>);</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno">  183</span>        std::vector&lt;double&gt; pos, neg;</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno">  184</span>        <span class="keywordflow">for</span>(std::size_t i=0; i&lt;prediction.size(); i++) {</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno">  185</span>            <span class="keywordflow">if</span>(!m_invert){</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno">  186</span>                <span class="keywordflow">if</span>(target(i) &gt; 0) </div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno">  187</span>                    pos.push_back(prediction.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(i)(column));</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno">  188</span>                <span class="keywordflow">else</span>  </div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno">  189</span>                    neg.push_back(prediction.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(i)(column));</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno">  190</span>            }<span class="keywordflow">else</span>{</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno">  191</span>                <span class="keywordflow">if</span>(target(i) &gt; 0)</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno">  192</span>                    pos.push_back(-prediction.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(i)(column));</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno">  193</span>                <span class="keywordflow">else</span></div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno">  194</span>                    neg.push_back(-prediction.<a class="code hl_function" href="group__shark__globals.html#ga0ea72a74a21d5ff59772516b83c4a58b">element</a>(i)(column));</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno">  195</span>            }</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno">  196</span>        }</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno">  197</span>        std::size_t m = pos.size();</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno">  198</span>        std::size_t n = neg.size();</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno">  199</span> </div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno">  200</span>        std::sort (pos.begin(), pos.end());</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno">  201</span>        std::sort (neg.begin(), neg.end());</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno">  202</span> </div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno">  203</span>        <span class="keywordtype">double</span> A = 0;</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno">  204</span>        <span class="keywordflow">for</span>(std::size_t i = 0, j = 0; i != m; i++) {</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno">  205</span>            A += j; </div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno">  206</span>            <span class="keywordflow">for</span>(std::size_t j = 0; j != n; j++) {</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno">  207</span>                <span class="keywordflow">if</span>(pos[i] &gt; neg[j]) </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno">  208</span>                    A++;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno">  209</span>                <span class="keywordflow">else</span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno">  210</span>                    <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno">  211</span>            }</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno">  212</span>        }</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno">  213</span> </div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno">  214</span><span class="preprocessor">#ifdef DEBUG</span></div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno">  215</span>        <span class="comment">// most naive implementation </span></div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno">  216</span>        <span class="keywordtype">double</span> verifyA = 0.;</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno">  217</span>        <span class="keywordflow">for</span>(std::size_t i=0; i&lt;m; i++) {</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno">  218</span>            <span class="keywordflow">for</span>(std::size_t  j=0; j&lt;n; j++) {</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno">  219</span>                <span class="keywordflow">if</span>(pos[i] &gt; neg[j]) verifyA++;</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno">  220</span>            }</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno">  221</span>        }</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno">  222</span>        <span class="keywordflow">if</span> (A!=verifyA) {</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno">  223</span>            <span class="keywordflow">throw</span>( <a class="code hl_class" href="classshark_1_1_exception.html" title="Top-level exception class of the shark library.">shark::Exception</a>( <span class="stringliteral">&quot;shark::WilcoxonMannWhitneyStatistic::eval: error in algorithm, efficient and naive implementation do no coincide&quot;</span>, __FILE__, __LINE__ ) );</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno">  224</span>        }</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno">  225</span><span class="preprocessor">#endif</span></div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno">  226</span> </div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno">  227</span>        <span class="keywordflow">return</span> -A / (n*m);</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno">  228</span>    }</div>
</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno">  229</span> </div>
<div class="foldopen" id="foldopen00230" data-start="{" data-end="}">
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"><a class="line" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#ad7be3ba6f121a686e6dcbeb87813599f">  230</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#ad7be3ba6f121a686e6dcbeb87813599f">eval</a>(<a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;LabelType&gt;</a> <span class="keyword">const</span>&amp; target, <a class="code hl_class" href="classshark_1_1_data.html" title="Data container.">Data&lt;OutputType&gt;</a>  <span class="keyword">const</span>&amp; prediction)<span class="keyword"> const </span>{</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno">  231</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(prediction.<a class="code hl_function" href="group__shark__globals.html#ga814e8b0028cc90dd2af69805e8f8a04d" title="Returns the total number of elements.">numberOfElements</a>() &gt;= 1,<span class="stringliteral">&quot;Empty prediction set&quot;</span>);</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno">  232</span>        <a class="code hl_define" href="_exception_8h.html#adce1f80097c69010f5eab2618fa2e971">SHARK_RUNTIME_CHECK</a>(<a class="code hl_function" href="group__shark__globals.html#ga6231b46b09731352a3cac40709a9625f" title="Return the dimensionality of a dataset.">dataDimension</a>(prediction) &lt; 3, <span class="stringliteral">&quot;Can not compute with more than two columns&quot;</span>);</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno">  233</span>        </div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno">  234</span>        std::size_t dim = <a class="code hl_function" href="group__shark__globals.html#ga6231b46b09731352a3cac40709a9625f" title="Return the dimensionality of a dataset.">dataDimension</a>(prediction);</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno">  235</span>        <span class="keywordflow">if</span>(dim == 1) </div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno">  236</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#aa2f5af11ed9351eb339943a4a0ef2e38" title="Computes Wilcoxon-Mann-Whitney statistic.">eval</a>(target, prediction, 0);</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno">  237</span>        <span class="keywordflow">else</span> <span class="keywordflow">if</span>(dim == 2) </div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno">  238</span>            <span class="keywordflow">return</span> <a class="code hl_function" href="classshark_1_1_negative_wilcoxon_mann_whitney_statistic.html#aa2f5af11ed9351eb339943a4a0ef2e38" title="Computes Wilcoxon-Mann-Whitney statistic.">eval</a>(target, prediction, 1);</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno">  239</span>        <span class="keywordflow">return</span> 0.;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno">  240</span>    }</div>
</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno">  241</span> </div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno">  242</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno">  243</span>    <span class="keywordtype">bool</span> m_invert;</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno">  244</span>};</div>
</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno">  245</span> </div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno">  246</span> </div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno">  247</span>}</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno">  248</span><span class="preprocessor">#endif</span></div>
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